I've only read of others breeding clownfiish, never tried it myself. If you really are interested in doing it, go out and get the book "Clownfishes" by Joyce Wilkerson as it's pretty much the bible on that subject. Here's what little I've gleaned from my reading:
The fry are miniscule and the first difficulty with them is sperating them from the main display aquarium. They will get killed in powerheads, filtration, eaten by shrimp/crabs/inverts/fish, etc within hours. Ideally the clowns lay eggs on something that is removable. Then 6-7 days after they're laid, you remove the eggs to the fry tank, they hatch and then you rear the fry there. Only use a sponge filter in the fry tank.
Next trouble is feeding the fry. They're so small they can only eat live phytoplankton at first and then live rotifers. Eventually they can be weaned onto frozen foods, but phyto and rots to start. Difficulty is you have to have big cultures of each before you try and rear the fry. Also the phyto and rots can really muck up water quality, so water changes are a must.
Those are the biggest challenges, but I'm sure there are plenty more. Lots of people do it successfully though, and many people sell tank-bred clowns. Heck, all the Perculas, Ocellaris, Skunk, and Clarkii clowns my LFS gets in are bred by a relatively local breeder